The connection coefficients allow to express one sequence of polynomials in terms of other one. Given any two general orthogonal polynomial sequences through of their recurrence coefficients, we present a general recursive method to compute the connection coefficients, using formal manipulation techniques in the Mathematica language. This method can be applied when one of the sequences is the canonical one. In several cases the observation of the formal results allows to establish a conjecture for the direct formula of those coefficients. After, those conjectures are prooved by induction. This method allow to obtain the connection coefficients in the cases of symmetrical, almost symmetrical, classical and semi-classical orthogonal polynomials.